Question #191652

What is the area with respect to the y axis of the curve x2 = 3y, from x = 0 to x = 4?


1
Expert's answer
2022-01-10T18:30:37-0500

Let us find the area AA with respect to the y-axis of the curve x2=3y,x^2 = 3y, from x=0x = 0 to x=4.x = 4. If x=0x=0then y=0.y=0. If x=4x=4 then y=163.y=\frac{16}3. It follows that x=±3y,x=\pm\sqrt{3y}, and using the symmetry of the curve about the y-axis, we get that

A=201633ydy=2323y320163=433(163)32=4334333=2569A=2\int\limits_0^{\frac{16}3}\sqrt{3y}dy =2\sqrt{3}\frac{2}3y^{\frac{3}2}|_0^{\frac{16}3} =\frac{4}3\sqrt{3}(\frac{16}3)^{\frac{3}2} =\frac{4}3\sqrt{3}\frac{4^3}{3\sqrt{3}} =\frac{256}{9} (sq. units).


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS